Question 1201530
<pre>
I have to simplify the following - all base 10 logarithms:
log(a)-1/2log(4a)
I get this far:
log(a) - log(4a)^1/2
log[a/(4a)^1/2]
but then I get stuck!
log(a) - {{{log((4a))^(1/2)}}}___{{{log((a/matrix(2,1, " ", (4a)^(1/2))))}}} <=== I got this far, but then I get stuck!
log(a) - {{{log((4a))^(1/2)}}} <==== Picking up from HERE!!
log(a) - {{{log((sqrt(4a)))}}}
log(a) - ({{{log((sqrt(4))) * (sqrt(a))}}})
log(a) - ({{{log((2)) * (sqrt(a))}}})
log(a) - {{{log((2sqrt(a)))}}}
log {{{(a/(2sqrt(a)))}}}
log ({{{(a*sqrt(a))/(2sqrt(a)sqrt(a))}}}) ----- RATIONALIZING denominator
log ({{{(a*sqrt(a))/(2a)}}}) ====> log ({{{(cross(a)*sqrt(a))/(2cross(a))}}}) ====> {{{highlight_green(matrix(1,4, log ((sqrt(a)/2)), ",", or, log ((sqrt(a))) - log ((2))))}}}</pre>